Well, for an example if you think about the product
(1+0,009)(1+0,008)⋅...⋅(1+0,001)=1,045879514 and
exp(0,009+...+0,001)=1,046...
I think the idea is to proof that first [itex]lim_{k→}∞[/itex] [itex]n_{k}=∞, then